Landing in England, Staying in Scotland - which rules should I follow? (July 2021)

My family and I (all US citizens) are traveling to Edinburgh, Scotland but our flight lands in London, England. We are taking a train from London to Edinburgh the day we arrive and we will quarantine at the flat we have rented there. We do not plan to spend much time in England.

The English quarantine website states:

Find where you can get the COVID-19 tests you need to take if you’re arriving in England from abroad.

You must book your tests before you travel and leave enough time for them to be delivered to your address in England.

The website then provides a list of various test providers with a large range of prices and locations:

https://www.find-travel-test-provider.service.gov.uk/test-type/amber

The Scottish website says:

If you’ve been in an amber list country in the 10 days before travelling to Scotland, you must:

• book and pay £170 for day 2 and day 8 COVID-19 travel tests - you must book your testing kit using the CTM Booking Portal – any other type of testing kit, such as free NHS kits or those sold by private businesses, cannot be used for these tests

It then links to a CTM portal to select your quarantine package which contains the following language:

For travellers arriving into England

and

For travellers arriving into Scotland

If I follow the "arriving into England" links then I just go back to the list of providers that the UK website linked to. If I follow the "arriving into Scotland" links then I am directed to the CTM North portal which requires you to select a port of entry in Scotland. As we did not enter the UK through a Scottish port, it would seem that this portal does not apply to us.

Do we need to follow the English rules or the Scottish rules?

The English test kits are a small fraction of the cost, and the Scottish portal would basically require me to falsify my travel itinerary. Most of the language I've found suggests strongly that my port of entry is what determines which rules I should follow, so I'm leaning strongly toward the English rules. But I don't want to violate Scottish law if they require all foreign travelers, regardless of entry point, to follow their rules.

Is there any official documentation or authoritative travel advice that clarifies this question for us? Perhaps we are expected to quarantine for 10 days in England (though this only appears to be required when traveling from a red list country)?